Chapter 10 FINANCIAL MARKETS AND FINANCIAL CRISES

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10 Chapter

FINANCIAL MARKETS AND FINANCIAL CRISES

The previous two chapters study the behavior of households and firms in partial-equilibrium settings. In Chapter 8, households divide their income between consumption and saving, taking the set of available assets and the distribution of their rates of returns as given. In Chapter 9, firms decide how much investment to undertake, taking the way that future profits are valued as given.

Financial markets are where these saving and investment decisions meet. In the absence of asymmetric information, externalities, and other imperfections, they play a central role in getting the economy to its Arrow-Debreu outcome. The signals sent by asset prices and state-contingent returns are what frame the partial-equilibrium problems that households and firms face. They therefore determine how households allocate their resources among consumption and holdings of various risky assets and what investment projects are undertaken. And it is the interaction of the demand and supply of risky assets that determines their prices. General equilibrium occurs when households and firms are optimizing taking prices as given, and where prices cause asset markets to clear. Section 10.1 presents a model of perfectly functioning financial markets in general equilibrium that shows this interplay between saving and investment decisions.

The main reason that macroeconomists are so interested in financial markets, however, is that they do not appear to function in this idealized way. There are at least four distinct issues related to financial markets that are important to macroeconomics.

The first is whether there are important macroeconomic propagation mechanisms operating through financial markets. With perfect financial markets, asset prices passively summarize all available information. But if there are imperfections in financial markets that cause departures from firstbest outcomes, those distortions may change endogenously in response to economic developments. As a result, they can magnify the macroeconomic effects of various types of shocks to the economy.

Sections 10.2 and 10.3 investigate this idea. Section 10.2 presents a microeconomicmodel of investment in the presence of asymmetric information

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Chapter 10 Financial Markets and Financial Crises

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between outside investors and entrepreneurs and examines the determinants and effects of the resulting distortions. It then shows that there are several channels that cause those distortions to be greater when the economy is weaker. Because the distortions reduce investment, their endogenous response to the state of the economy magnifies the macroeconomic effects of shocks a mechanism that is known as the financial accelerator. Then in Section 10.3, we will examine some microeconomic evidence about the importance of financial-market imperfections to investment.

The second issue concerns whether departures of financial markets from the Arrow-Debreu baseline not only magnify the effects of other disturbances, but can also be an independent source of shocks to the economy. In particular, Section 10.4 is devoted to the issue of possible excess volatility of asset prices. In perfect financial markets, the price of any asset is the rational expectation given the available information of the present value of the asset's future payoffs using the stochastic discount factor that arises from agents' marginal utilities of consumption; the price of the asset changes only if there is new information about its payoffs or about the stochastic discount factor. Section 10.4 examines the possibility that this assumption might fail. It shows that the forces pushing asset prices toward fundamentals if they depart are not unlimited, and analyzes several factors that limit their strength. It also describes how movements in asset prices not driven by fundamentals can affect macroeconomic outcomes. Section 10.5 addresses the issue of whether the possibilities described in Section 10.4 are merely hypothetical or whether there is evidence that they are important in practice.

A third macroeconomic subject raised by financial markets and the possibility of financial-market imperfections is financial crises. One might expect that a large financial system in an economy with millions of participants would change smoothly in response to economic developments. In fact, however, financial markets are subject to convulsions not only at the level of individual assets and financial institutions, but at the level of broad swaths of the financial system. One notable episode occurred in the Great Depression, when the economic downturn and repeated waves of panics led to the failure of one-third of U.S. banks. For decades, the conventional wisdom was that such worldwide financial crises were a thing of the past. But in the fall of 2008, this view was proven wrong. Lehman Brothers, a major investment bank, declared bankruptcy in September. In the aftermath, equity prices fell by more than 25 percent in just four weeks; spreads between interest rates on conventional but slightly risky loans and those on the safest and most liquid assets skyrocketed; many borrowers were unable to borrow at any interest rate; and economies around the world went into severe recessions.

Financial crises are the subject of Sections 10.6 through 10.8. The first of these presents the classic Diamond Dybvig model of the possibility of a self-fulfilling run on a financial institution that would otherwise be solvent. The second addresses the issue of how financial market disruptions and failures can spread among financial institutions. And the third discusses

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Chapter 10 FINANCIAL MARKETS AND FINANCIAL CRISES

some microeconomic evidence that sheds light on the macroeconomic effects of crises.

The final issue concerns the social value of financial markets. Private marginal products in financial markets can be either bigger or smaller than social marginal products. For example, someone who channels funds from small savers to a poor entrepreneur with the potential to become the next Thomas Edison or Steve Jobs will probably capture only a tiny part of the social value of the resulting inventions. On the other hand, someone who makes an enormous profit by buying an undervalued asset whose price would otherwise have risen a few seconds later probably has almost no effect on any actual investment decisions, and so has negligible social product.

Although this issue is fascinating and important, we will not pursue it. McKinnon (1973) and others argue that the financial system has important effects on overall investment and on the quality of the investment projects that are undertaken, and thus on economies' growth over extended periods. But the development of the financial system may be a by-product rather than a cause of growth; and factors that lead to the development of the financial system may affect growth directly. As a result, this argument is difficult to test. Nonetheless, there is at least suggestive evidence that financial development is important to growth (for example, Jayaratne and Strahan, 1996; Levine and Zervos, 1998; Rajan and Zingales, 1998; Levine, 2005). Likewise, Banerjee and Newman (1993) and Buera, Kaboski, and Shin (2011) argue that financial-market imperfections can lead to large inefficiencies in both human- and physical-capital investment, and that this misallocation has large effects on development.

There is even less evidence about whether too many resources are devoted to the financial sector in advanced economies. Budish, Cramton, and Shim (2015) present compelling evidence that efforts to increase trading speed are close to pure rent-seeking with little social value. But whether this description fits with much of how other resources in the financial sector are used is not clear. Philippon and Reshef (2012) present evidence that compensation in finance in the United States in recent decades is puzzlingly high, and Philippon (2015) finds that the large improvements in information technology and other types of technological progress do not appear to have increased the efficiency of the U.S. financial sector over the past hundred years. But again, this does not come close to resolving the question of whether too many resources are devoted to the financial sector.

10.1 A Model of Perfect Financial Markets

This section presents a model of perfectly functioning financial markets to show how the interaction of consumer preferences and the set of possible investments determine what investment projects are undertaken and how claims on the projects' output are valued.

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10.1 A Model of Perfect Financial Markets

461

Assumptions and Equilibrium Conditions

The economy lasts for two periods. A representative household has an endowment E of the economy's sole good in period 1 and no endowment in period 2. It maximizes the expected value of its lifetime utility, which is given by

V = U (C1) + U (C2), > 0, U (?) > 0, U (?) < 0,

(10.1)

where Ct is the household's consumption in period t.

All period-2 output comes from investments undertaken in period 1.

There are N possible investment projects. The output of each project is

potentially uncertain. Specifically, there are S possible states of the world

in period 2. If quantity Ki of period-1 output is devoted to project i , it

produces Ris Ki in period 2 in state s (where Ris 0 for all i and s). We

let s denote the probability of state s occurring; the s's satisfy s 0

and

S s=1

s

=

1.

The

Ki 's

cannot

be

negative.

It

is

convenient

to

think

of each investment project as being undertaken by a distinct firm. Finally,

the economy is perfectly competitive: households and firms are price-takers.

It is straightforward to write down the conditions that characterize the

equilibrium of this economy. Because there are complete markets and no

imperfections, we can describe the equilibrium in terms of Arrow-Debreu

commodities that is, claims on period-2 output in the various states of the

world. Specifically, let qs be the price, in units of period-1 output, of a claim

on one unit of perod-2 output in state s. Then equilibrium is a set of prices,

{qs}, investment decisions, {Ki }, and consumption decisions, C1 and {C2s }, with three properties.

First, households must be maximizing their utility subject to their budget

constraint. The budget constraint is

S

C1 + qsC2s = E.

s=1

(10.2)

Utility maximization requires that reducing C1 by a small amount and using the savings to increase C2s does not affect lifetime utility. This yields the Euler equation.

U

(C1)

=

1 qs

s

U

(C2s )

for all s.

We can rearrange this as

qs

=

U s U

(C

s 2

)

(C1)

for all s.

(10.3) (10.4)

That is, in equilibrium the price of a claim on output in state s equals the product of the probability that the state occurs and the marginal utility of consumption in that state relative to consumption today.

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Chapter 10 FINANCIAL MARKETS AND FINANCIAL CRISES

Second, there must be no unexploited profit opportunities. The cost of

investing marginally more in project i , in terms of period-1 consumption, is

just1. The payoff is the revenues from selling the state-contingent output,

which is

S s =1

qs

Ris.

If

a

strictly

positive

amount

is

invested

in

the

project,

the payoff to investing marginally more must equal the cost. And if nothing

is invested in the project, the payoff from the first unit of investment must

be less than or equal to the cost. Thus we have

S

= 1

s=1 qs Ris 1

if Ki > 0 if Ki = 0

for all i.

(10.5)

Notice that since there is a full set of Arrow-Debreu commodities, there is no risk in undertaking the project: although the amount that the project produces depends on the state, claims on output in all states are sold in period 1.

Finally, markets must clear. The market-clearing condition in period 1 is

N

C1 + Ki = E.

i =1

(10.6)

And the market-clearing condition for claims on period-2 output in state s is

N

Ki

Ris

=

C

s 2

i =1

for all s.

(10.7)

The number of equilibrium conditions is 1 (from [10.2]), plus S (from [10.3] or [10.4]), plus N (from [10.5]), plus 1 (from [10.6]), plus S (from [10.7]). The unknowns are the S qs's, the S C2's, the N Ki 's, and C1. The number of equations exceeds the number of unknowns by 1 because of Walras's law.

Discussion

From firms' perspective, this model is little different from the partialequilibrium model of investment we studied in Chapter 9, particularly the model of investment under uncertainty in Section 9.7. And from households' perspective, the model is similar to the partial-equilibrium model of consumption in the presence of risky assets in Section 8.5. But because both investment and consumption are endogenous in the current model, the marginal utility of consumption in different states, and hence the payoff to investment projects in different states, is now endogenous.

The only assets with net supplies that are strictly positive are claims on the output of the investment projects that are undertaken. But although the net supplies of any other potential financial assets are zero, one can still think of markets where some agents can sell them and others buy them. The

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10.2 Agency Costs and the Financial Accelerator

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price of any asset (including ones without positive net supplies) depends

on the pricing kernel of this economy, which is determined by the marginal

utility of consumption in different states. That is, the price of an asset with

payoff in state s of xs is

S s=1

qs xs .

Two

potentially

interesting

assets

are

debt and insurance. The price of riskless debt that is, an asset that pays 1

unit regardless of the state is

S s=1

qs

.

The

price

of

insurance

against

state

s

occurring that is, an asset that pays 1 unit in state s and 0 otherwise is qs.

Of course, since all households are the same, in equilibrium we will not

observe some agents selling these assets and others buying them. But with

heterogeneity in preferences or income, we would.

Also, notice that trade in financial assets can get the economy to the

Walrasian outcome without there literally being Arrow-Debreu commodi-

ties with all transactions taking place at the beginning of time. In the model,

where agents are homogeneous, the Arrow-Debreu allocation can be

achieved through equity markets where claims on firms' output are traded.

With heterogeneous agents, additional assets, such as insurance contracts,

would also be needed.

Crucially, because all markets are perfectly competitive, information is

symmetric, and there are no externalities, the equilibrium is Pareto effi-

cient. If we enriched the model to allow for the arrival of new information

(for example, about the probabilities of the different states or the returns

to investment projects in different states), there would be changes in as-

set prices, but they would be efficient. And the only reason for there to

be sudden large changes in prices would be the sudden arrival of major

news.

There are numerous possible extensions that would not affect these cen-

tral features of the model. Examples include additional periods, hetero-

geneity among households, adjustment costs in investment, and a role for

other inputs into production (most obviously, labor supplied by house-

holds). None of these would alter the messages that financial markets are

where households and firms meet to efficiently share risk and determine

the level and composition of investment. Rather than pursuing those ex-

tensions, the rest of the chapter turns to settings where financial markets

have more significant consequences.

10.2 Agency Costs and the Financial Accelerator

Introduction

In the models of Chapter 9 and Sections 10.1, all parties are equally well informed, and so financial markets function efficiently. Potential investments are valued according to their state-contingent payoffs using the prevailing

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Chapter 10 FINANCIAL MARKETS AND FINANCIAL CRISES

stochastic discount factor. As a result, they are undertaken if their value exceeds the cost of acquiring and installing the necessary capital.

In fact, however, firms are much better informed than potential outside investors about their investment projects. Outside financing must ultimately come from individuals. These individuals usually have little contact with the firm and little expertise concerning the firm's activities. In addition, their stakes in the firm are usually low enough that their incentive to acquire relevant information is small.

Because of these problems, institutions such as banks, mutual funds, and bond-rating agencies that specialize in acquiring and transmitting information play central roles in financial markets. But even they can be much less informed than the firms or individuals in whom they are investing their funds. The issuer of a credit card, for example, is usually much less informed than the holder of the card about the holder's financial circumstances and spending habits. In addition, the presence of intermediaries between the ultimate investors and firms means that there is a two-level problem of asymmetric information: there is asymmetric information not just between the intermediaries and the firms, but also between the individuals and the intermediaries (Diamond, 1984).

Asymmetric information creates agency problems between investors and firms. Some of the risk in the payoff to investment is usually borne by the investors rather than by the firm; this occurs, for example, in any situation where there is a possibility that the firm may go bankrupt. When this is the case, the firm can change its behavior to take advantage of its superior information. It can only borrow if it knows that its project is particularly risky, for example, or it can choose a high-risk strategy over a low-risk one even if this reduces overall expected returns. Thus asymmetric information can distort investment choices away from the most efficient projects. In addition, asymmetric information can lead the investors to expend resources monitoring the firm's activities, and the managers or entrepreneurs running the firm to devote less than the socially optimal amount of effort to the firm. Thus again, asymmetric information imposes costs.

This section presents a simple model of asymmetric information and the resulting agency problems and discusses some of their effects. We will find that when there is asymmetric information, investment depends on more than just interest rates and profitability; such factors as investors' ability to monitor firms and firms' ability to finance their investment using internal funds also matter. We will also see that asymmetric information changes how interest rates and profitability affect investment and that it magnifies the effects of shocks to the economy.

Assumptions

An entrepreneur has the opportunity to undertake a project that requires 1 unit of resources. The entrepreneur has wealth of W, which is less than 1.

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Thus, he or she must obtain 1 - W units of outside financing to undertake the project. If the project is undertaken, it has an expected output of , which is positive. is heterogeneous across entrepreneurs and is publicly observable. Actual output can differ from expected output, however; specifically, the actual output of a project with an expected output of is distributed uniformly on [0,2 ]. Since the entrepreneur's wealth is all invested in the project, his or her payment to the outside investors cannot exceed the project's output. This limit on the amount that the entrepreneur can pay to outside investors means that the investors must bear some of the project's risk.

To keep things simple, we assume that the entrepreneur and outside investors are risk-neutral, and that there is a technology with no risk or asymmetric information that yields a rate of return of r for sure. We also assume that the outside investors are competitive. These assumptions have several implications. First, the project is socially desirable if and only if the expected rate of return is greater than r ; that is, the requirement for a social planner to want the project to be undertaken is > 1 + r . Second, because the entrepreneur can invest at the risk-free rate, he or she undertakes the project if the difference between and the expected payments to the outside investors is greater than (1 + r )W. And third, competition implies that in equilibrium, outside investors' expected rate of return on any financing they provide to the entrepreneur is r .

The key assumption of the model is that entrepreneurs are better informed than outside investors about their projects' actual output. Specifically, an entrepreneur observes his or her output costlessly; an outside investor, however, must pay a cost c to observe output. c is assumed to be positive; for convenience, it is also assumed to be less than expected output, .

This type of asymmetric information is known as costly state verification (Townsend, 1979). In studying it, we will see not only how asymmetric information affects investment outcomes, but also how it shapes financial contracts. There are other types of information asymmetries, such as asymmetric information about the riskiness of projects or about entrepreneurs' actions, that may be more important than costly state verification in practice. However, they have broadly similar implications concerning distortions and the amplification of shocks, so it is instructive to study these issues through the lens of the simpler costly-state-verification model.

The Equilibrium under Symmetric Information

In the absence of the cost of observing the project's output, the equilibrium is straightforward. Entrepreneurs whose projects have an expected payoff that exceeds 1 + r obtain financing and undertake their projects; entrepreneurs whose projects have an expected output less than 1 + r do not. For the projects that are undertaken, the contract between the entrepreneur

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